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Pointwise identification of the elastic properties in thoracic aneurysm tissue

Frances M. Davis1 · Yuanming Luo3 · Stéphane Avril1 · Ambroise Duprey1,2 · Jia Lu3
1École Nationale Supérieure des Mines Saint-Étienne
2 Hôpital Nord, Cardiovascular Surgery Service, CHU de Saint-Étienne
3 Mechanical Engineering, University of Iowa

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Abstract.

Introduction: Ascending thoracic aortic aneurysms (ATAAs) are focal, asymmetric dilatations of the aortic wall which are prone to rupture. If an ATAA does spontaneously rupture, the result is almost invariably death [1]. To identify potential rupture locations in advance, it is necessary to consider the inhomo- geneity of the ATAA at the millimeter scale [2,3]. Towards this end, we have developed a combined experimental and computational approach using bulge inflation tests, digital image correlation (DIC), and an inverse membrane approach to characterize the pointwise stress, strain, and elastic properties of the ATAA.

Materials and Methods: By coupling the bulge inflation tests with DIC to obtain full-field displacement measurements, we are able to compute the strain locally [3]. Using the full-field displacement data, the wall stresses were calculated using an isogeometric inverse method [4]. Forward and inverse membrane elements were developed, replacing the finite element interpolation with a NURBS representation. Using the computed full field stress-strain data (Fig. 1a), the pointwise distribution of mechanical properties for the ATAA specimens were identified (Fig. 1b). Finally, a forward analysis was performed using ho- mogenous, elementwise, and pointwise distribution of the mechanical properties and the resulting errors in the predicted displacement were compared (Fig. 1c).

Results: The results of the forward analysis using homogenous, elementwise, and pointwise properties indi- cate that the spatial variation in the material parameters must be accounted for in order to accurately replicate the behavior of the ATAA. Notably for the pointwise method themean error in predicting the stress was less than 2% whereas for the homogenous case the error was approximately 20%. The mean error in nodal displacement was on the order of 0.2%.

Conclusion: In this work, we determined, for the first time, the heterogeneous distribution of mechanical proper- ties in the ATAA. In the future, we will combine this study on the local mechanical properties with an imaging technique such as multiphoton microscopy to identify a relationship between the local stress-strain response and the underlying structural behavior.

References

  1. Juvonen T et al. Ann Thorac Surg. 63:1533-1545,1997.
  2. Zhao X et al. J Biomech Eng, 133(5):51008, 2011.
  3. Romo A et al. J Biomech, 47(3):607-616, 2014.
  4. Lu J et al. Biomech. Model. Mechanobiol., 7(6):477-86, 2008.